Metamorphic tiling patterns based on zonohedra

Claim 1

A method of producing metamorphic tiling patterns for various design applications and comprising: a plurality of transformed polygons derived from a base tiling pattern composed of plane-filling base polygons wherein said transformed polygons are obtained by applying geometric transformations on the edges of said base polygons wherein each said transformed polygon is a geometric transformation of the adjacent transformed polygon and said plurality of transformed polygons displays a gradual transformation of the tiling pattern from one portion of the pattern to another, where said geometric transformations are binary combinations of n distinct geometric transformations performed on edges of said base polygons, where the said plurality of said transformed polygons cover a surface of an underlying zonohedron network composed of contiguous parallelogram faces and defined by a projection of an n-dimensional cube having edges parallel to n directions, such that each direction is coupled with an associated geometric transformation, and where n is any number greater than 3, where the said metamorphic tiling pattern is derived by using the method steps comprising the following: selecting said base tiling pattern composed of plane-filling 4-sided base polygons of desired proportions and angles, projecting said n-dimensional cube onto said base tiling pattern, identifying sets of said base polygons as vertex-polygons corresponding to the vertices of said projected n-dimensional cube, edge-polygons corresponding to the edges of said projected n-dimensional cube, and face-polygons corresponding to all remaining polygons which are not vertex- and edge-polygons, performing a first transformation on each said vertex-polygon whereby n independent geometric transformations are selected and their combinations applied to all said vertex-polygons thereby creating a set of transformed vertex-polygons, selecting a sub-set of said transformed vertex-polygons corresponding to the vertices of said contiguous parallelogram faces of said zonohedron network, performing a second transformation whereby all said edge-polygons corresponding to the edges of the said zonohedron network are transformed by gradual incremental transformations between said transformed vertex-polygons thereby creating a set of transformed edge-polygons, performing a third transformation whereby all said face-polygons corresponding to the faces of the said zonohedron network are transformed by gradual incremental transformations between said transformed vertex- and edge-polygons, where said method steps are applied systematically over the entire surface of the said zonohedron network to generate said metamorphic tiling pattern.

Claim 2

A method of producing metamorphic tiling patterns for various design applications and comprising: a plurality of transformed polygons derived from a base tiling pattern composed of plane-filling base polygons wherein said transformed polygons are obtained by applying geometric transformations on the edges of said base polygons wherein each said transformed polygon is a geometric transformation of the adjacent transformed polygon and said plurality of transformed polygons displays a gradual transformation of the tiling pattern from one portion of the pattern to another, where said geometric transformations are binary combinations of n distinct geometric transformations performed on edges of said base polygons, where the said plurality of said transformed polygons cover a surface of an underlying zonohedron network composed of contiguous parallelogram faces and defined by a projection of an n-dimensional cube having edges parallel to n directions, such that each direction is coupled with an associated geometric transformation, and where n is any number greater than 3, where the said metamorphic tiling pattern is derived by using the method steps comprising the following: selecting said base tiling pattern composed of plane-filling 4-sided base polygons of desired proportions and angles, projecting said n-dimensional cube onto said base tiling pattern, identifying sets of said base polygons as vertex-polygons corresponding to the vertices of said projected n-dimensional cube, edge-polygons corresponding to the edges of said projected n-dimensional cube, and face-polygons corresponding to all remaining polygons which are not vertex- and edge-polygons, performing a first transformation on each said vertex-polygon whereby n independent geometric transformations are selected and their combinations applied to all said vertex-polygons thereby creating a set of transformed vertex-polygons, selecting a sub-set of said transformed vertex-polygons corresponding to the vertices of said contiguous parallelogram faces of said zonohedron network, performing a second transformation whereby all said edge-polygons corresponding to the edges of the said zonohedron network are transformed by gradual incremental transformations between said transformed vertex-polygons thereby creating a set of transformed edge-polygons, performing a third transformation whereby all said face-polygons corresponding to the faces of the said zonohedron network are transformed by gradual incremental transformations between said transformed vertex- and edge-polygons, where said method steps are applied systematically over the entire surface of the said zonohedron network to generate said metamorphic tiling pattern.